Prace Naukowe Instytutu Maszyn, Napędów i Pomiarów ElektrycznychNr 70 Politechniki Wrocławskiej Nr 70Studia i Materiały Nr 34 2014

induction motor, Direct Torque Control,Flux-Space-Vector Modulation, field weakening control

Khanh NGUYEN THAC*, Teresa ORLOWSKA-KOWALSKA**

CONTROL OF THE DTC-FSVM BASEDINDUCTION MOTOR DRIVE IN A WIDE SPEED RANGE

In this paper the direct flux and torque control structure based on Flux-error Space VectorModulation (DTC-FSVM) has been analyzed and compared to a classical DTC-SVM system. Thecontrol structures have been tested in a wide speed range including field weakening algorithm basedon the voltage and current limits of the voltage inverter and the induction motor. The proposed con-trol strategies are verified through simulation with a 3 kW induction motor drive.

1. INTRODUCTION

Induction motors (IM) due to their operational reliability, small size and low costin comparison to DC motors and permanent magnet synchronous motors, are con-tinuously most popular among the electrical motors applied in the industry [6], [9].However, the complicated mathematical model of the induction motor entails thatcomplex control methods and structures must be used to obtain the dynamic behaviorof these drives similar to classical DC motor drives with cascade control structure.Presently the quite matured control methods, which ensure excellent dynamics of theIM drive, are Field Oriented Control (FOC) and Direct Torque Control (DTC) meth-ods [2]–[4], [6], [9], [13]. Both techniques can be considered as high performancevector controllers based on the decoupling of motor flux and torque. The DTC sys-tems, which were first introduced in the middle of 1980s, ensure a very quick andprecise torque control response with relatively simple control structure based onhysteresis controllers for the stator flux and electromagnetic torque [3], [9], [13].However, classical DTC method has several disadvantages, from which the most_________

* Department of Electrical and Electronic Engineering, Hanoi University of Mining and Geology,Duc Thang Ward, Bac Tu Liem District, Hanoi, Vietnam, e-mail: nguyenthackhanh@humg.edu.vn

** Institute of Electrical Machines, Drives and Measurements, Wroclaw University of Technology,ul. Smoluchowskiego 19, 50-372 Wroclaw, Poland, e-mail: teresa.orlowska-kowalska@pwr.wroc.pl

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important is a variable switching frequency. Nowadays, apart from classical DTCmethod, based on the voltage switching table (ST-DTC), some new direct torquecontrol techniques have been developed [4]–[6]. The overview of the DTC methodswas presented in [6].

Simple structure and very good dynamic behavior are main features of classicalST-DTC based schemes. On contrary, the DTC techniques based on Space-Vector--Modulation ensure constant switching frequency, but the control structure is morecomplicated and first of all contains PI controllers and requires vector transformation ofcoordinate systems. In these schemes the reference voltage vector is generated based onthe torque and flux errors. This reference voltage vector is next utilized for generatinginverter switching states using the principle of SVM (Space Vector Modulation).

Recently a novel approach of the direct flux and torque control with SVM has beenproposed [12], which consists in replacing the reference voltage vector by referencestator flux-error vector, which is called Flux-error Space Vector Modulation (F-SVM).The stator flux-error vector is used as a main variable for calculation IGBT switching-on times of the VSI (Voltage Source Inverter).

The effectiveness of this control concept has been tested in this paper in a widespeed range of the IM drive system, especially in the field-weakening (FW) region. Inthese tests the FW method, which ensures maximum DC bus voltage utilization is used.Taking into account a voltage limit and a current limit of inverter and induction motor inFW region (as in [7], [8]), a control strategy for FW-operation-based DTC-FSVMmethod with maximum torque capability algorithm is presented. The control schemeutilizes the stator flux components as control variables and decreases the d-componentof the stator flux as soon as the voltage corresponding to the maximum torque achiev-able at a given speed tends to exceed the maximum voltage.

2. PRINCIPLE OF THE FLUX-ERROR SPACE VECTOR MODULATION

The stator flux vector control method relies directly on the Faraday’s law. Underspace vector theory, this law can be written as, dtdT sNind ψu = , i.e. the rate of changeof the stator flux vector sψ is equal to the induced voltage vector ( indu ). If statorwinding resistance is negligible, the induced voltage is equal to the applied statorvoltage ( su ).

In discrete time domain, this equation can be interpreted as

ssNsss TT τuuΔψ == , (1)

where, sT is a sampling time period in [s] and bNT Ω=1 is the nominal time constantin [s], therefore sτ is defined as relative sampling time period in [p.u.].

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A vector displacement ∗sΔψ is based on an error between actual ( )ksψ and pre-

dicted )1( +ksψ stator flux vectors (Fig. 1a) [12]; it can be obtained by applying a volt-

age vector ∗su for a time sτ (Fig. 1b). In three phase voltage space vector controlled

VSI, the stator flux-error vector can be defined as:

( )00ττττ ′+′+′== ∗∗ uuuuΔψ LLRRsss , (2)

where: LR uu , are the right and left adjacent active voltage vectors in a given sec-tor; 0u – the zero voltage vectors; 0,, τττ ′′′ LR normalized ( NTt /=′τ ) switch-ing-on times of the right, left and the zero voltage vectors respectively.

In Fig. 1, the stator flux-error vector can be defined by modulus ∗∗ =Δ ssψ Δψ

and argument sγ . In a steady state, with the assumption that stator flux sψ andstator frequency are constants, the stator flux-error vector components can be cal-culated as:

⎟⎠⎞

⎜⎝⎛=Δ= ∗∗

sssss τωψ21sin2ψΔψ , (3)

.21

21

21

21

ετωπ

ετωππγ

++=

⎥⎦

⎤⎢⎣

⎡+⎟

⎠⎞

⎜⎝⎛ −−=

ss

sss

(4)

β

α

s sω τ

ε

εsγ

sω

( )1s k+ψ

( )s kψ

s∗Δψ

2s sω τ

1234 5 6

α

βs Rτ u

sωs∗Δψ

L Lτ ′u

)

sβψ ∗Δ

sαψ ∗Δ

23R L dc

R RR s

s N

LL

N

ut tT T

tT

τ τ

τ

= =

′ = =

′ =

u u

sγ

s Lτ u

R Rτ ′u

0 0τ ′u

Fig. 1. Trajectory of the stator flux-error vector: a) definition of the stator flux-error vector,b) stator flux-error vector in specific voltage sector

a) b)

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For a small value of the sampling time interval, the product ssτω will be very

small. Therefore, ssss τωτω21

21sin ≈⎟

⎠⎞

⎜⎝⎛ . For example, at angular velocity ][1 p.u.=sω ,

if sampling time period sT is 1 ms, then the difference between actual value

⎟⎠⎞

⎜⎝⎛

ssτω21sin and its approximation ssτω

21 is less than 0.2%. So, the stator flux-error

modulus in equation (3) can be simplified as:

ssss ψτωψ =Δ ∗ . (5)

Similarly to the well know Voltage Space Vector Modulation (V-SVM) method, withreference stator voltage vector as an input information, in Flux Space Vector Modulation(F-SVM) method the stator flux-error ∗

sΔψ can be used as an input information.In the presented F-SVM, three operation regions are used (like in V-SVM strategy):

linear region, overmodulation (divided into region I and region II) and six-step mode.An operation region is defined by modulation index (6):

dcs

si

uM

τπ

ψ2

∗Δ= (6)

where, ∗Δ sψ – stator flux-error vector module; dcu – DC link voltage.Operation regions dependent on modulation index values are shown in the Table 1.

Table 1. Operation regions dependent on modulation indexes

Operation regions

OvermodulationLinear

Region I Region IISix-step

907.00 <≤ iM 952.0907.0 <≤ iM 1952.0 <≤ iM 1=iM

In the linear operation region, switching-on times can be calculated as follows.

( )( )3sin

3sin3π

αππ

−= i

sRMTt , (7a)

( )( )3sinsin3πα

πi

sLMTt = , (7b)

( )LRs ttTt +−=0 . (7c)

7

α

β

s∗Δψ

sω

s Lτ u

α

3dc

suτ

α

β

s s sτ∗ ∗=Δψ usβψ ∗Δ

)b

3π

sαψ ∗Δsαψ ∗Δ

sβψ ∗Δ

α

α

23R L dc

R RR s

s N

LL

N

ut tT T

tT

τ τ

τ

= =

′ = =

′ =

u u

R Rτ ′u s Rτ u R Rτ ′u

L Lτ ′u

R Ruτ ′0 0τ ′u 0 0τ ′u

Fig. 2. Flux-error vector modulation in the linear region

In the Fig. 2 an illustration of the Flux-error Vector Modulation in the linear re-gion is given. The overmodulation and six-step operation modes are used in the drivesystem to enable the full DC link voltage utilization of the converter (details on theovermodulation algorithm was shown in [13]).

3. DIRECT TORQUE CONTROLWITH FLUX-ERROR SPACE VECTOR MODULATION

In the closed-loop flux and torque control methods based on Stator-Flux-Orientation (SFO), the reference stator flux vector is used, therefore its angular fre-quency, rmss ωωω += (or position angle, ∫= dtT ssNss ωγ 1 ) must be known. The

mechanical speed, mω can be received from the encoder (or well-known speed esti-mators), so only slip speed must be estimated. There exist different methods for slipspeed estimation, which are presented in the references [9], [13]. Thus, the stator fluxvector position can be presented as:

( ) sskssss γγγ Δ+= −1 , (8)

where: ( )1−kssγ – previous angle position in the last sampling time,dynstatssssss γγγ Δ+Δ=Δ – change of the stator flux vector position angle in the

current sampling time,statssγΔ – stationary change of the stator flux vector position angle,dynssγΔ – dynamic change of the stator flux vector position angle.

General stator flux vector movement and its components are illustrated in Fig. 3.

a) b)

8

( )s kψ

( )1s k−ψ

α

β

( )1ss kγ −

statssγΔ

( )ss kγ

ssω

ssγΔ

Fig. 3. Stator flux vector position components

The predictive direct stator flux vector control algorithm is proposed in [1], whichis equipped with one PID controller. The aim of the controller is to estimate the slipangle, slipγΔ . Another predicted value is a mechanical speed, predicmω , which multi-

plied by a sampling time, sτ , makes mechanical angle, mγΔ . As a result, change ofthe stator flux vector angle can be obtained as a sum of the mechanical and slip angles,

slipmss γγγ Δ+Δ=Δ and stator flux vector position (8) can be obtained as:

( ) slipmkssss γγγγ Δ+Δ+= −∗

1 . (9)

Block diagram of this algorithm is shown in Fig. 4.

Predict orwi t h PIDcont rol l er

mω∗

ˆmω

slipγΔ

sψ ∗

r θ∠

-α β

sαψ ∗

sβψ ∗

ssγΔ

sτpredicmωmγΔ ( )1ss kγ −

ssγ ∗

Fig. 4. Prediction of the shifted stator flux vector angle

In the reference [11] authors proved that derivative of the electromagnetic torqueis proportional to the instantaneous slip angular frequency, which means we can usea PI controller to control the slip frequency in order to control the electromagnetictorque.

In the case of closed-loop flux and torque control and under constant flux( const=rψ ), the stator flux vector position angle ∗

ssγ can be calculated as:

( )∫∫ +==∗t

rmN

t

ssN

ss dtT

dtT

00

11 ωωωγ (10)

9

Many schemes used this idea for calculation of the synchronous speed ssω or sta-tor flux vector position angle ssγ [6, 12] (Fig. 5).

rω∗em∗

PI−

ˆ emsψ ∗

mω

ssω∗

∫ ssγ ∗

-α β

sαψ ∗

sβψ ∗

r θ∠

Fig. 5. Slip angular frequency generated by torque controller

Therefore, the flux position angle can be rewritten as:

( ) slipmkm

t

rN

t

mN

ss dtT

dtT

γγγωωγ Δ+Δ+=+= −∗∗ ∫∫ 1

00

11 (11)

In the steady-state, under discrete time domain, the stationary angle positionchanges can be calculated as:

sssss ωτγ =Δ stat . (12)

When the load torque changes, predicted flux vector position angle( )∫ ∗∗ += dtT rmNss ωωγ 1 deviates from the actual position angle ( )∫ += dtT rmNss ωωγ 1 ,

and thus the dynamic angle referred to the torque change is produced dynssγδψ Δ=Δ :

( )∫ −=−=Δ ∗∗ dtT rr

Nssssss ωωγγγ 1dyn (13)

Equation (13) shows, that we can obtain the dynamic position angle by a PI control-ler from difference of the slip angular frequency, rrrω ωωδ −= ∗ [5, 10] (see Fig. 6).

sψ ∗

sτSlipcal.

rω∗em∗

rω PI

ssγΔ

Slipcal.

statssω

dynssγΔrωδ

−em

rψ

mω ( )1ss kγ −

-α β

sαψ ∗

sβψ ∗

ssγ ∗statssγΔ r θ∠

Fig. 6. Dynamic flux vector position generated by slip controller

10

In the Fig. 6, slip calculation blocks are based on the following expression [9]:

er

rr mr

2ψω = . (14)

To choose the best scheme for stator flux vector position generating, in this sectionall presented schemes are tested and compared under steady-state and dynamicalmodes, in a wide speed range. The simulation results for above schemes in high speedregion are presented in Fig. 7, for step changes of the load torque (from 0.5s to 0.7sthe load torque is reduced 50% from the previous steady state value.)

0.1

0.2

0.3

0.4

0.1

0.2

0.3

0.4

0.1

0.2

0.3

0.4

0.4

0.42

0.44

0.46

0.4

0.42

0.44

0.46

0.4

0.42

0.44

0.46

2.07

2.08

2.09

2.07

2.08

2.09

2.07

2.08

2.09

0.4 0.6 0.8

1.86

1.87

Time [s]0.4 0.6 0.8

1.86

1.87

Time [s]0.4 0.6 0.8

1.86

1.87

Time [s]

1)a 1)b 1)c

) Scheme in Fig. 6c) Scheme in Fig. 5b) Scheme in Fig. 4a

2)a 2)b 2)c

3)a 3)b 3)c

4)a 4)b 4)c

Lmem

Lmem

Lmem

sψ ˆsψ sψ

sω sω sω

∗mω

mω

∗mω

mω

∗mω

mω

Fig. 7. Simulation results: torque (a1–c1), flux (a2–c2), stator frequency (a3–c3) and speed (a4–c4)transients under load torque changes

These simulation results show that the dynamics of the third scheme (Fig. 6) isvery good. As a result, stator flux, electromagnetic torque and speed quickly respondto the reference or load torque changes if compared with other schemes (see Fig. 7c).

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According to the above analysis, the block diagram of the DTC-FSVM structurewas next tested, presented in Fig. 8. This structure includes the calculation of the sta-tor flux position angle according to the scheme in Fig. 6, due to its best dynamicalperformance. Additionally the field weakening algorithm with torque limit was used inthe chosen DTC-FSVM structure.

dcu

si

CS

AS

BS

VSI

+−

=

~

sαψ ∗Δ

sβψ ∗Δssγ ∗

Polar toCartesian

sψ ∗

Estimator

sαψ ∗

sβψ ∗

ˆssγ

sτSlipcal.

rω∗

em∗

ˆrω PI

Slipcontroller

sγΔ

Slipcal.

statsω

dynssγΔ

statssγΔ

rωδ

IMSpeed sensor

suˆ sβψˆ sαψ

−

mω

ˆ emˆ em

−

−

mωˆ rψ

ˆ rψ

MTFWalgorithm

limem

s calculationu

dcu

Fig. 8. Chosen DTC-FSVM control of IM drive

rωsup

rψ

em

maxem

bsω csω

Constant torqueregion

Constant powerRegion

(FW region I) Constant slipRegion

(FW region II )

sω0

1em ∝

ω

max breakdown torque

normal torque

rotor flux

power

stator voltage

rotor (slip) speed

e

e

r

s

r

m

m

ψ

p

u

ω

−

−

−

−

−

−

2max1ω

∝em

Fig. 9. Control characteristics of the induction motor in constant and weakened flux regions

The operating speed range of the IM drive can be divided in three sub-regions:constant torque region ( sbs ωω < ), constant power region ( scssb ωωω <≤ ) and con-stant slip frequency region ( scs ωω ≥ ) [6], as is shown in Fig. 9 (where scsb ωω , arebase and critical stator angular speeds).

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In the block scheme of Fig. 9, the Torque-Maximized Field Weakening (TMFW)algorithm described detail in [7], [8] is used. In this algorithm, only mechanical speed( mω ) and DC link voltage ( dcu ) are input variables, therefore it is not dependent onthe reference frame (RFO or SFO) chosen for its development.

4. TEST RESULTS

In the following figures, simulation results are presented to show the comparisonbetween two DTC structures under the same MTFW algorithm and operation condi-tions, such as voltage, load torque and reference speed. The test results for the clas-sical DTC-SVM structure (with V-SVM) are plotted in the left hand side of eachfigure, while the results of the DTC-FSVM scheme are presented in the right handside, respectively. All tests were performed for 3.0kW, 1400 rpm induction motorand following per-unit parameters: rs = 0.0707, rr = 0.0637, xs = xr = 1.9761,xM = 1.8780, ψrN = 0.8 (calculated according [12]. Simulations were performed forthe same voltage and current limit constraints ( 64.0max =u [p.u.], 5.1max =i [p.u.]),thus the value of the base and critical speeds were obtained as 55.0=mbω [p.u.] and

27.1=mcω [p.u.].

0 1 2 3

-0.5

0

0.5

0 1 2 3

-0.5

0

0.5

0.74 0.76 0.78 0.80.515

0.52

0.525

0.74 0.76 0.78 0.80.515

0.52

0.525

0.74 0.76 0.78 0.80.6

0.65

0.7

Time [s]0.74 0.76 0.78 0.8

0.6

0.65

0.7

Time [s]

mω∗ mω

Lmem

mω∗

Lm em

)a )b

)c )d

)e )f

mω

DTC-SVM DTC-FSVM

Fig. 10. Simulation results: start up, steady state at ωm = 0.52 [p.u.]and breaking cycle in both directions: (a, b) reference and motor speed, load and motor torque,

(c–f) zoom in the speeds and torques at steady state

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In Fig. 10 simulation results under linear speed reference ramp start-up and steadystate at 52.0=∗

mω [p.u.] speed (constant torque region), for maximum load torque

NL mm = and breaking cycle in both directions are shown.In the next Fig. 11 simulation results under linear speed reference ramp start-up

and steady state at the speed 0.1=∗mω [p.u.] (FW region I) and breaking cycle in both

directions are presented. Maximum load torque satisfies constant power condition,

NmbLm mm ωω =∗ .

0 1 2 3-1

0

1

0 1 2 3-1

0

1

0.74 0.76 0.78 0.8

0.998

1

1.002

0.74 0.76 0.78 0.8

0.998

1

1.002

0.74 0.76 0.78 0.8

0.35

0.4

Time [s]0.74 0.76 0.78 0.8

0.35

0.4

Time [s]

mω∗ mω

Lmem

mω∗

Lmem

)a )b

)c )d

)e )f

mω

DTC-SVM DTC-FSVM

Fig. 11. Simulation results: Start up, steady state at ω∗m = 1.0 [p.u.]

and breaking cycle in both directions: (a, b) reference and motor speed, load and motor torque,(c–f) zoom in the speeds and torques at steady state

It can be seen from Fig. 10 and Fig. 11, that speed and torque transients of theDTC-FSVM scheme are much smoother then for the DTC-SVM scheme.

Next, the simulation results for the FW region II are presented in Fig. 12. In thistest, linear speed reference ramp start-up, next steady state operation at the speed

8.1=∗mω [p.u.] and then breaking process, with maximum steady state load torque equal

0.175 [p.u.] were applied for both DTC systems.Under these operation conditions, the load torque is close to the torque limit (see

Fig. 12e, f), therefore the PI controllers are working in nonlinear mode. As a result,both systems will be working in the overmodulation mode. Operation under over-modulation mode and saturation of the PI controllers cause that the DTC-SVM drive

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cannot obtain maximum torque generation and reference speed also (see Fig. 12c). Incomparison, the DTC-FSVM can work in dynamic mode, so in this test the VSI oper-ates in six-step mode at steady state and system can obtain the desired speed value(see Fig. 12d).

So it is clearly seen that DTC-FSVM control structure with the flux position anglecalculated according scheme of Fig. 6 give much better dynamical and static perform-ance in the torque and speed control in the whole speed range, including overmodula-tion and six-step mode.

0 1 2 30

1

2

0 1 2 30

1

2

1 1.5 21.6

1.7

1.8

1 1.5 21.6

1.7

1.8

1 1.5 2

0.15

0.2

0.25

Time [s]1 1.5 2

0.15

0.2

0.25

Time [s]

mω∗

mω

Lm

em

mω∗

Lm

)a )b

)c )d

)e )f

mω

DTC-SVM DTC-FSVM

limem lim

emem

Fig. 12. Simulation results: ramp start up, steady state at ω∗m =1.8 [p.u.]

and braking for two structures: (a, b) reference and motor speed, load and motor torque,(c–f) zoom in the speeds and torques at steady state

6. CONCLUSION

In this paper, the analysis of the flux-error space vector modulation (F-SVM)and three difference concepts of the flux vector position generation in the DTC--FSVM control structure of the induction motor drive are presented. The coordi-nate transformations, PI torque and flux controllers, which are specific for theclassical DTC-SVM (with voltage space vector modulation) are eliminated andonly one PI controller for slip speed is used. So, the presented configuration isvery simple. In this control structure the torque-maximized flux weakening(TMFW) algorithm can be used and applied for advanced high speed applications

15

of VSI-fed IM drives, as for spindle and traction application. Test results shownthat, the obtained drive systems can operate in a very wide speed range and haveexcellent torque response as well as smooth transients in the whole range of speedif compared with classical DTC-SVM structure.

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